Exactly Solvable Model for the Kondo Problem

Abstract

A model for magnetic impurities in metals is introduced and solved exactly. It treats longitudinal impurity-electron coupling in the long-time approximation of the x-ray threshold problem and treats transverse spin-density operators in a fermion representation. For antiferromagnetic coupling, the magnetization in field $H$ vanishes as ${H}^{2{J}_{\ensuremath{\parallel}}}$ and saturates when $H$ is of order ${(\frac{J_{\ensuremath{\perp}}^{}{}_{}{}^{2}}{{J}_{\ensuremath{\parallel}}})}^{\frac{1}{2}{J}_{\ensuremath{\parallel}}}$ ${J}_{\ensuremath{\parallel}}$ and ${J}_{\ensuremath{\perp}}$ are longitudinal and transverse exchange constants). For ferromagnetic coupling, the free moment is only slightly renormalized.